Resolver {left(1/3right)}^2+{left(1/3right)}^-2+{left(-1/3right)}^3+3^-2

$${ \left( \frac{ 1 }{ 3 } \right) }^{ 2 } + { \left( \frac{ 1 }{ 3 } \right) }^{ -2 } + { \left(- \frac{ 1 }{ 3 } \right) }^{ 3 } + { 3 }^{ -2 }$$

Avaliar

$$\frac{248}{27}\approx 9,185185185$$

Passos Para a Resolução

Calcule \frac{1}{3} elevado a 2 e obtenha \frac{1}{9}.

$$\frac{1}{9}+\left(\frac{1}{3}\right)^{-2}+\left(-\frac{1}{3}\right)^{3}+3^{-2}$$

Calcule \frac{1}{3} elevado a -2 e obtenha 9.

$$\frac{1}{9}+9+\left(-\frac{1}{3}\right)^{3}+3^{-2}$$

Some \frac{1}{9} e 9 para obter \frac{82}{9}.

$$\frac{82}{9}+\left(-\frac{1}{3}\right)^{3}+3^{-2}$$

Calcule -\frac{1}{3} elevado a 3 e obtenha -\frac{1}{27}.

$$\frac{82}{9}-\frac{1}{27}+3^{-2}$$

Subtraia \frac{1}{27} de \frac{82}{9} para obter \frac{245}{27}.

$$\frac{245}{27}+3^{-2}$$

Calcule 3 elevado a -2 e obtenha \frac{1}{9}.

$$\frac{245}{27}+\frac{1}{9}$$

Some \frac{245}{27} e \frac{1}{9} para obter \frac{248}{27}.

$$\frac{248}{27}$$

Fatorizar

$$\frac{2 ^ {3} \cdot 31}{3 ^ {3}} = 9\frac{5}{27} = 9,185185185185185$$